Spinal V2b neurons reveal a role for ipsilateral inhibition in speed control

The spinal cord contains a diverse array of interneurons that govern motor output. Traditionally, models of spinal circuits have emphasized the role of inhibition in enforcing reciprocal alternation between left and right sides or flexors and extensors. However, recent work has shown that inhibition also increases coincident with excitation during contraction. Here, using larval zebrafish, we investigate the V2b (Gata3+) class of neurons, which contribute to flexor-extensor alternation but are otherwise poorly understood. Using newly generated transgenic lines we define two stable subclasses with distinct neurotransmitter and morphological properties. These V2b subclasses synapse directly onto motor neurons with differential targeting to speed-specific circuits. In vivo, optogenetic manipulation of V2b activity modulates locomotor frequency: suppressing V2b neurons elicits faster locomotion, whereas activating V2b neurons slows locomotion. We conclude that V2b neurons serve as a brake on axial motor circuits. Together, these results indicate a role for ipsilateral inhibition in speed control

Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom

For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be calculated using only one UPO sampled from the ensemble. Evidence to support this conclusion is obtained by generating the ensemble by Monte Carlo calculation for a statistical mechanical model described by a space-time Hamiltonian that is expressed in terms of Floquet exponents of UPOs. This result allows us to interpret the recent interesting discovery that statistical properties of turbulence can be obtained from only one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].Comment: 4 pages, 1 figure. In order to clarify generality of our result and the role of a large number of degrees of freedom, a brief subsection was adde

Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction

We study a non-ergodic transition in a many-body Langevin system. We first derive an equation for the two-point time correlation function of density fluctuations, ignoring the contributions of the third- and fourth-order cumulants. For this equation, with the average density fixed, we find that there is a critical temperature at which the qualitative nature of the trajectories around the trivial solution changes. Using a method of dynamical system reduction around the critical temperature, we simplify the equation for the time correlation function into a two-dimensional ordinary differential equation. Analyzing this differential equation, we demonstrate that a non-ergodic transition occurs at some temperature slightly higher than the critical temperature.Comment: 8 pages, 1 figure; ver.3: Calculation errors have been fixe

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle-point. The theoretical calculation explains results of numerical simulations.Comment: 18pages, 17figures.The version 2, in which minor errors have been fixed, will be published in Phys. Rev.

Infiltrative microgliosis: activation and long-distance migration of subependymal microglia following periventricular insults

BACKGROUND: Subventricular microglia (SVMs) are positioned at the interface of the cerebrospinal fluid and brain parenchyma and may play a role in periventricular inflammatory reactions. However, SVMs have not been previously investigated in detail due to the lack of a specific methodology for their study exclusive of deeper parenchymal microglia. METHODS: We have developed and characterized a novel model for the investigation of subventricular microglial reactions in mice using intracerebroventricular (ICV) injection of high-dose rhodamine dyes. Dynamic studies using timelapse confocal microscopy in situ complemented the histopathological analysis. RESULTS: We demonstrate that high-dose ICV rhodamine dye injection resulted in selective uptake by the ependyma and ependymal death within hours. Phagocytosis of ependymal debris by activated SVMs was evident by 1d as demonstrated by the appearance of rhodamine-positive SVMs. In the absence of further manipulation, labelled SVMs remained in the subventricular space. However, these cells exhibited the ability to migrate several hundred microns into the parenchyma towards a deafferentation injury of the hippocampus. This "infiltrative microgliosis" was verified in situ using timelapse confocal microscopy. Finally, supporting the disease relevance of this event, the triad of ependymal cell death, SVM activation, and infiltrative microgliosis was recapitulated by a single ICV injection of HIV-1 tat protein. CONCLUSIONS: Subependymal microglia exhibit robust activation and migration in periventricular inflammatory responses. Further study of this population of microglia may provide insight into neurological diseases with tendencies to involve the ventricular system and periventricular tissues

The order-disorder transition in colloidal suspensions under shear flow

We study the order-disorder transition in colloidal suspensions under shear flow by performing Brownian dynamics simulations. We characterize the transition in terms of a statistical property of time-dependent maximum value of the structure factor. We find that its power spectrum exhibits the power-law behaviour only in the ordered phase. The power-law exponent is approximately -2 at frequencies greater than the magnitude of the shear rate, while the power spectrum exhibits the $1 / f$-type fluctuations in the lower frequency regime.Comment: 11 pages, 10 figures, v.2: We have made some small improvements on presentation

An order parameter equation for the dynamic yield stress in dense colloidal suspensions

We study the dynamic yield stress in dense colloidal suspensions by analyzing the time evolution of the pair distribution function for colloidal particles interacting through a Lennard-Jones potential. We find that the equilibrium pair distribution function is unstable with respect to a certain anisotropic perturbation in the regime of low temperature and high density. By applying a bifurcation analysis to a system near the critical state at which the stability changes, we derive an amplitude equation for the critical mode. This equation is analogous to order parameter equations used to describe phase transitions. It is found that this amplitude equation describes the appearance of the dynamic yield stress, and it gives a value of 2/3 for the shear thinning exponent. This value is related to the mean field value of the critical exponent $\delta$ in the Ising model.Comment: 8 pages, 2 figure

Two Langevin equations in the Doi-Peliti formalism

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \rightleftarrows X+X$ is investigated as an illustrative example.Comment: 14page

Comparison of observed and simulated cement microstructure using spatial correlation functions

金沢大学理工研究域環境デザイン学系The microstructure of cement pastes, as revealed by SEM-BSE image analysis, was compared with a simulated structure generated by the University of Twente version of the CEMHYD3D hydration simulation model. The spatial array of unhydrated cement particles was simulated by the model. However, spatial features in capillary pore structure obtained by the simulation are different from the observed microstructure. This disagreement in the spatial structure is to be expected since there are fundamental differences in porosity as represented by the two methods. Only coarse pores are detected in the SEM examination while the total capillary porosity and its whole spatial distribution are virtually simulated in the model. A subset of the visible pores must be different in spatial statistics from the universal set of total porosity. Care must therefore be taken in interpreting agreement between simulation output and microscopically observed microstructure in images. © 2009 Elsevier Ltd. All rights reserved

Energy dissipation and violation of the fluctuation-response relation in non-equilibrium Langevin systems

The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance condition is not satisfied in nonequilibrium systems. Even in this case, it has been found that for a class of Langevin equations, there exists an equality between the extent of violation of the fluctuation-response relation in the nonequilibrium steady state and the rate of energy dissipation from the system into the environment [T. Harada and S. -i. Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. Since this equality involves only experimentally measurable quantities, it serves as a proposition to determine experimentally whether the system can be described by a Langevin equation. Furthermore, the contribution of each degree of freedom to the rate of energy dissipation can be determined based on this equality. In this paper, we present a comprehensive description on this equality, and provide a detailed derivation for various types of models including many-body systems, Brownian motor models, time-dependent systems, and systems with multiple heat reservoirs.Comment: 18 pages, submitted to Phys. Rev.